Smoothie sales are on fire. the price is $3 for an adult and $1 for children. if 260 smoothies were sold for a total of 675.00 how many adults purchased smoothies? how many children?

Step-by-step explanation:

If "a" represents the number of adult smoothies sold, then 260-a is the number of smoothies sold to children. The total revenue is ...

  3a +1(260-a) = 675

  2a +260 = 675 . . . . . . eliminate parentheses

  a + 130 = 337.5 . . . . . . divide by 2

  a = 207.5 . . . . . . . . smoothies sold to adults

  260-a = 52.5 . . . . . smoothies sold to children

For the given numbers, this is the way it works out. The "half" values suggest there is a typo somewhere, possibly in the curriculum material. Talk to your teacher about this one.

this answer is !

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt